Both extensions imply restrictions on the mobility of the excitation, which is partial in the case of vector charge theory and complete in the scalar charge theory [1]}.
Fractons are commonly understood as belonging to the second type of realization of the higher rank gauge theory, namely the scalar charge theory. This type of new quasiparticles lies on the boundary of several theoretical research activities, wherever immobility plays an important role (amorphousness in solids [2]}, [3]}, [4]} and in computational systems [5]}, [6]}, [7]},
long-term entanglement [8]}, [9]}, [10]}, for instance).
In this paper we would like to focus on the consequences of dealing with a gauge field \(A_{ij}\)  with a tensorial nature, which necessarily shares its birth certificate with Linearized Gravity (LG) [11]}, as it is apparent from the two cases mentioned above. It is readily seen, indeed, that for a particular choice of the vector parameter of the spatial diffeomorphism transformation (REF )
\(\Phi _i = (\partial _i\Phi )/2\) 
